Adaptive Independent Metropolis-Hastings by Fast Estimation of Mixtures of Normals

TL;DR

This paper introduces a fast, reliable adaptive independent Metropolis-Hastings algorithm that employs a mixture of normals as a proposal, updating frequently to improve sampling efficiency and convergence.

Contribution

It presents a novel adaptive Metropolis-Hastings method using mixture of normals with frequent updates, ensuring convergence and enhanced performance.

Findings

Efficient sampling demonstrated on real and simulated data

Convergence to target distribution proven under specific conditions

Algorithm outperforms traditional methods in speed and reliability

Abstract

We construct an adaptive independent Metropolis-Hastings sampler that uses a mixture of normals as a proposal distribution. To take full advantage of the potential of adaptive sampling our algorithm updates the mixture of normals frequently, starting early in the chain. The algorithm is built for speed and reliability and its sampling performance is evaluated with real and simulated examples. Our article outlines conditions for adaptive sampling to hold and gives a readily accessible proof that under these conditions the sampling scheme generates iterates that converge to the target distribution.